two part question.
goal - turn off lights after 5 minutes of inactivity in room.
do you not have anything setup?
these are automations. They go in the automation section.
correct. i have not bought anything ever for home automation.
Do you even have home assistant running? If not, answering the second question is kinda pointless as you need to understand how HA works to know where to put things. It’s hard to understand how HA works without knowing Yaml or the UI.
As for your first question. You just need to decide what type of communication protocal you want to use. There are many: Zigbee, Zwave, through wifi, rf, mqtt w/ various devices. The list goes on. The 2 ‘major’ protocols that most people use are Zwave and Zigbee. I personally use zwave. It requires zwave devices and a zwave usb stick to communicate with the devices. You linked in your post a zwave device, so if you were to purchase them, you’d need the zwave usb stick. Instead of the stick you can also get a hub. There are a number of hubs out there. Too many to list. I think you should take a look at the hardware section of these forums and do some research on the pitfalls of each protocol and then decide for yourself.
i do not have home assistant running. how do I do that?
Have you checked the getting started section?
Do you have any of the supported Hardware for running HASSIO lying around the house? You might find that it is easier to start with HASSIO.
Another option is do you have a NAS drive such as one of the Synology devices?